?latm6

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?latm6

Generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues.

Syntax

void slatm6 (lapack_int *type, lapack_int *n, float *a, lapack_int *lda, float *b, float *x, lapack_int *ldx, float *y, lapack_int *ldy, float *alpha, float *beta, float *wx, float *wy, float *s, float *dif);

void dlatm6 (lapack_int *type, lapack_int *n, double *a, lapack_int *lda, double *b, double *x, lapack_int *ldx, double *y, lapack_int *ldy, double *alpha, double *beta, double *wx, double *wy, double *s, double *dif);

void clatm6 (lapack_int *type, lapack_int *n, lapack_complex_float *a, lapack_int *lda, lapack_complex_float *b, lapack_complex_float *x, lapack_int *ldx, lapack_complex_float *y, lapack_int *ldy, lapack_complex_float *alpha, lapack_complex_float *beta, lapack_complex_float *wx, lapack_complex_float *wy, float *s, float *dif);

void zlatm6 (lapack_int *type, lapack_int *n, lapack_complex_double *a, lapack_int *lda, lapack_complex_double *b, lapack_complex_double *x, lapack_int *ldx, lapack_complex_double *y, lapack_int *ldy, lapack_complex_double *alpha, lapack_complex_double *beta, lapack_complex_double *wx, lapack_complex_double *wy, double *s, double *dif);

Include Files

mkl.h

Description

The ?latm6 routine generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and also reciprocal condition numbers for all eigenvalues and the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues.

There two kinds of test matrix pairs:

(A, B)= inverse(YH) * (Da, Db) * inverse(X)

Type 1:

Type 2:

In both cases the same inverse(YH) and inverse(X) are used to compute (A, B), giving the exact eigenvectors to (A,B) as (YH, X):

where a, b, x and y will have all values independently of each other.

Input Parameters

type: Specifies the problem type.
n: Size of the matrices A and B.
lda: The leading dimension of a and of b.
ldx: The leading dimension of x.
ldy: The leading dimension of y.
alpha, beta: Weighting constants for matrix A.
wx: Constant for right eigenvector matrix.
wy: Constant for left eigenvector matrix.

Output Parameters

a: Array, size lda*n. On exit, a contains the n-by-n matrix initialized according to type.
b: Array, size lda*n. On exit, b contains the n-by-n matrix initialized according to type.
x: Array, size ldx*n. On exit, x contains the n-by-n matrix of right eigenvectors.
y: Array, size ldy*n. On exit, y is the n-by-n matrix of left eigenvectors.
s: Array, size (n). s[i - 1] is the reciprocal condition number for eigenvalue i .
dif: Array, size(n). dif[i - 1] is the reciprocal condition number for eigenvector i .

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?latm6